It is a vector question?

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Answer 1 · 2018-05-01T21:10:17

$p= 6.5 \ \$ , and $q= -1.5$ ,

We have:

$bbvec(OA) = ((0),(2),(-3)) \ \$ , $bbvec(OB) = ((2),(5),(-2)) \ \$ and $bbvec(OC) = ((3),(p),(q))$

And so we can compute the vector $bbvec(AB)$ ,

$bbvec(AB) = bbvec(OB) - bbvec(OA) = ((2),(5),(-2)) - ((0),(2),(-3)) = ((2),(3),(1))$

Similarly, we can compute the vector $bbvec(BC)$ ,

$bbvec(BC) = bbvec(OC) - bbvec(OB) = ((3),(p),(q)) - ((2),(5),(-2)) = ((1),(p-5),(q+2))$

As ABC is a straight line then, for some constant $lamda$ ,

$bbvec(AB) = lamda bbvec(BC)$

Hence we have:

$((2),(3),(1)) = lamda ((1),(p-5),(q+2))$

Equating components:

$R1: 2 = lamda$ ,
$R2: 3=lamda(p-5) => p-5=3/2 => p= 6.5$ ,
$R3: 1=lamda(q+2) => q+2=1/2 => q= -1.5$ ,